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PreprintCC BY 4.0arXiv

Noncommutative commutant lifting, interpolation, and shift-invariant subspaces

  • Sibaprasad Barik
  • Samir Panja
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Abstract

We establish a Sarason-type commutant lifting theorem in the framework of noncommutative Drury-Arveson space and apply it to solve the noncommutative Nevanlinna-Pick interpolation problem on the noncommutative row ball. In particular, it recovers the classical Nevanlinna-Pick interpolation theorem over the open unit disc. We also provide a Beurling-Lax-Halmos-type characterization of shift-invariant subspaces of noncommutative Drury-Arveson space using dilation theoretic technique.

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Cite

BibTeXRIS
BibTeX
@misc{barik2026noncommutative,
  title = {{Noncommutative commutant lifting, interpolation, and shift-invariant subspaces}},
  author = {Sibaprasad Barik and Samir Panja},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11410},
  eprint = {2609.11410},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11410},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Noncommutative commutant lifting, interpolation, and shift-invariant subspaces
AU  - Sibaprasad Barik
AU  - Samir Panja
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11410
UR  - https://arxiv.org/abs/2609.11410
AB  - We establish a Sarason-type commutant lifting theorem in the framework of noncommutative Drury-Arveson space and apply it to solve the noncommutative Nevanlinna-Pick interpolation problem on the noncommutative row ball. In particular, it recovers the classical Nevanlinna-Pick interpolation theorem over the open unit disc. We also provide a Beurling-Lax-Halmos-type characterization of shift-invariant subspaces of noncommutative Drury-Arveson space using dilation theoretic technique.
ER  -